Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

A Compact Defected Ground Microstrip Device with Photonic Bandgap Effects

Filters and other devices using photonic bandgap (PBG) theory are typically implemented in microstrip lines by etching periodic holes on the ground plane of the microstrip. The period of such several holes corresponds to nearly half the guided wavelength of the transmission line. In this paper we study the effects of miniaturization of the PBG device by meandering the microstrip line about one single hole in the ground plane. A comparison of the S-parameters and dispersion behavior of the modified geometry and a conventional PBG device with a straight microstrip line shows that these devices have similar behaviors.

Agoralla : avauksia ympäristöasiantuntijoiden vuorovaikutusprosesseista

Ympäristöasiantuntijoiden vuorovaikutusta on tutkittu agoralla (antiikin tori). Se on julkinen tila, jossa markkinat, politiikka, tiede ja yhteiskunta kohtaavat. Tutkimus kuuluu yhteiskuntatieteellisen ympäristötutkimuksen alaan, mutta siinä hyödynnetään myös tulevaisuudentutkimusta. Työn motivaationa on ollut tekijän monitieteinen koulutustausta: yhteiskuntatieteilijä ja luonnontieteilijä. Miten ja miksi vuorovaikutus eri asiantuntijoiden välillä on haasteellista ja merkityksellistä esimerkiksi metsän biodiversiteetin vähenemisen ehkäisemiseksi. Keskeisiä käsitteitä ovat asiantuntijuus, vuorovaikutus, tiedon luotettavuusja kontekstisidonnaisuus, Väitöskirja koostuu neljästä eri asiantuntijuustarinasta. Ensimmäinen (luku 2) perustuu haastatteluihin suomalaisten ja saksalaisten bio- ja yhteiskuntatietelijöiden käsityksistä luonnosta ja ympäristöstä. Tutkimusongelmana on luonnontieteilijöiden ja yhteiskuntatieteilijöiden Suomessa ja Saksassa ”kulttuurierot” luonnon ja ympäristön käsitteellistämisessä. Johtopäätöksenä on, että aistittu luonto, ympäröivä ympäristö sekä ihmisen muokkaama elinympäristö eivät tunne selkeitä tiede- eikä maanrajoja. Tämä luku toimii ponnahduslautana konstruktioiden taakse vuorovaikutuksen haasteisiin. Kirjan toinen tarina (luku 3) perustuu haastatteluihin suomalaisten metsän biodiversiteettiasiantuntijoiden vuorovaikutuksesta. Tutkimusongelman lähtökohtana on metsän biodiversiteetin väheneminen ja tästä seuraavat polittisetkin vuorovaikutustilanteet. Miten konteksti vaikuttaa eri asiantuntijoiden vuorovaikutukseen ja mitä tästä seuraa? Analyysin päätulos on implisiittisen, vahvasti kontekstisidonnaisen asiantuntijatiedon hyödyntämisen tarve ja voimavara metsän biodiversiteetin vähenemisen ennaltaehkäisemiksi. Kolmas tarina asiantuntijuudesta (luku 4) perustuu Etelä-Suomen metsien suojelutoimikunnassa (Metso) tehtyihin havainnointeihin. Tutkija on näin ollut itse eräänlaisella torilla havainnoijana. Tutkimusongelmana on ”ohipuhuminen”, tiedon luotettavuus ja implisiittien tiedon hyväksyttävyys. Johtopäätöksenä on asiantuntijuuden vahva kontekstisidonnaisuus hetkeen ja paikkaan ja yhteisen kielen (vrt. transdisiplinaarisuus) löytyminen yhteisen tavoitteen saavuttamiseksi. Merkittäviä välineitä vuorovaikutuksen onnistumiseen ovat esimerkiksi yhteinen vahva tavoitetila, interkatio, joka koskee läsnä olevia ihmisiä ei instituutioita sekä fasilitaattorin vahva rooli tulkkina ja välittäjänä. Neljäs tarina (luku 5) vie agoran konkretiaan. Tässä luvussa on kehitetty eläytymiskävely- menetelmää, jossa fasilitaattori (tutkija) johdattaa Espoon keskuksessa hallinnon, politiikan, asukkaiden ja konsultin edustajat aistimaan ja tulkitsemaan alueen sosiaalista tilaa, toiminnallisuutta ja elämyksellisyyttä. Ongelmana on aistimaailman asiantuntemuksen hyödyntämättömyys yhdyskuntasuunnittelun välineenä mm. asiantuntijoiden vuorovaikutuksen välineenä. Menetelmäkehitys on aluillaan, mutta jo tässä tapauksessa käy ilmi, että jaettu tila, jaetut aistikokemukset konkreettisella kävelyllä avaavaat vuorovaikutuksen uusiin ulottuvuuksiin, jossa implisiittiselle asiantuntemukselle annetaan sijansa vuorovaikutuksessa ja tätä kautta voidaan vaikuttaa myös tehtäviin päätöksiin, toimenpiteisiin. Johtopäätöksissä (luku 6) korostuu implisiittisen asiantuntijuuden merkitys. Onnistunut vuorovaikutteinen toiminta eri asiantuntijoiden kesken esimerkiksi erilaisia ympäristöongelmia –ja ilmiöitä ratkottaessa ja pohdittaessa vaatii vuorovaikutusosaamista. Tutkimuksen lopuksi suositellaan esimerkiksi ennakkoluulottomia avauksia agoralla. Asiantuntijuus ei ole yksi ja vain asiaatuntevuus on mahdollista. Agora on jatkuvassa liikkeessä ja juuri siinä piilee voimavara tulevaisuuden haasteisiin erilaisilla rajapinnoilla. Avainsanat: asiantuntijuus, vuorovaikutus, tieto, konteksti, agora

Helsingin Östersundomin pienvesien kartoitus

The area of Östersundom (29,1 square kilometers) was attached to Helsinki in the beginning of the year 2009. Östersundom is formed mostly from the municipality of Sipoo, and partly from the city of Vantaa. Nowadays Östersundom is still quite rural, but city planning has already started, and there are plans to develop Östersundom into a district with 45 000 inhabitants. In this study, the headwaters, streams and small lakes of Östersundom were studied to produce information as a basis for city planning. There are six main streams and five small lakes in Östersundom. The main methodology used in this study was the examination of the physical and the chemical quality of the water. The hygienic quality of the water was also studied. It was also examined whether the waters are in their natural state, or have they been treated and transformed by man. In addition, other factors affecting the waters were examined. Geographical information data was produced as a result of this work. Östersundom is the main area looked at in this study, some factors are examined in the scope of the catchment areas. Water samples were collected in three sampling periods: 31.8 4.9.2009, 3. 4.2.2010, and 10. 14.4.2010. There were 20 sampling points in Östersundom (5 in small lakes, 15 in streams). In the winter sampling period, only six samples were collected, from which one was taken from a small lake. Field measurements associated with water sampling included water temperature, oxygen concentration, pH and electoral conductivity. Water samples were analyzed in the Laboratories of Physical Geography in the University of Helsinki for the following properties: total suspended solids (TSS), total dissolved substances (TDS), organic matter, alkalinity, colour, principal anions and cations and trace elements. Metropolilab analyzed the amount of faecal coliform bacteria in the samples. The waters in Östersundom can be divided to three classes according to water quality and other characteristics: the upper course of the streams, the lower course of the streams and the small lakes. The streams in their upper course are in general acidic, and their acid neutralization capacity is low. The proportion of the organic matter is high. Also the concentrations of aluminium and iron tend to be high. The streams in the lower course have acidity closer to neutral, and the buffering capacity is good. The amounts of TSS and TDS are high, and as a result, the concentrations of many ions and trace elements are high as well. Bacteria were detected at times in the streams of the lower course. Four of the five small lakes in Östersundom are humic and acidic. TSS and TDS concentrations tend to be low, but the proportion of organic matter is often high. There were no bacteria in the small lakes. The fifth small lake (Landbonlampi) differs from the others by its water colour, which is very clear. This lake is very acidic, and its buffering capacity is extremely low. Compared to the headwaters in Finland in general, the concentrations of many ions and trace elements are higher in Östersundom. On the other hand, the characteristics of water were different according to the classification upper course streams, lower course streams, and small lakes. Generally, the best water quality was observed in the stream of Gumbölenpuro and in the lakes Storträsk, Genaträsk, Hältingträsk and Landbonlampi. Several valuable waters in their natural state were discovered from the area. The most representative example is the stream of Östersundominpuro in its lower course, where the stream flows through a broad-leaf forest area. The small lakes of Östersundom, and the biggest stream Krapuoja, with its meandering channel, are also valuable in their natural state.

Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.

Development and studies on microstrip detector

We report development of gas microstrip detectors using thin film and lithography techniques. The detectors were tested for their performance for X-rays (5.9 keV) and a maximum gas gain of similar to 13,000 and best resolution of similar to 12% was obtained. Factors affecting gain and resolution were investigated. The detectors were tested for their one-dimensional position sensitivity. Meandering resistive strips were used for charge division method. A position resolution of 0.48 mm was obtained.

Spatiotemporal chaos in a model for CO oxidation on Pt(110)

We present numerical studies of a model for CO oxidation on the surface of Pt(110) proposed in Ref. 1. The model shows several interesting regimes, some of which exhibit spatiotemporal chaos. The time series of the CO concentration at a given point consists of a sequence of pulses. We concentrate on interpulse intervals theta and show that their distribution P(theta) approaches a delta function continuously as the system goes from a state M, with meandering spirals, to a state S, with spatially frozen spiral cores. This should be verifiable experimentally.

A summer monsoon pump to keep the Bay of Bengal salty

The Bay of Bengal receives a large influx of freshwater from precipitation and river discharge. Outflow of excess freshwater and inflow of saltier water is required to prevent the bay from freshening. Relatively fresh water flows out of the bay along its boundaries and inflow of saltier water occurs via the Summer Monsoon Current (SMC), which flows eastward from the Arabian Sea into the bay. This saltier water, however, slides under the lighter surface water of the bay. Maintaining the salt balance of the bay therefore demands upward mixing of this saltier, subsurface water. Here, we show that an efficient mechanism for this mixing is provided by upward pumping of saltier water in several bursts during the summer monsoon along the meandering path of the SMC. Advection by currents can then take this saltier water into the rest of the basin, allowing the bay to stay salty despite a large net freshwater input.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Tectono-geomorphic and environmental set-up deduced during deposition of Mio-Pleistocene sediments in NW Himalaya, India

Detailed pedofacies characterization along-with lithofacies investigations of the Mio-Pleistocene Siwalik sediments exposed in the Ramnagar sub-basin have been studied so as to elucidate variability in time and space of fluvial processes and the role of intra- and extra-basinal controls on fluvial sedimentation during the evolution of the Himalayan foreland basin (HFB). Dominance of multiple, moderately to strongly developed palaeosol assemblages during deposition of Lower Siwalik (similar to 12-10.8 Ma) sediments suggest that the HFB was marked by Upland set-up of Thomas et al. (2002). Activity of intra-basinal faults on the uplands and deposition of terminal fans at different times caused the development of multiple soils. Further, detailed pedofacies along-with lithofacies studies indicate prevalence of stable tectonic conditions and development of meandering streams with broad floodplains. However, the Middle Siwalik (similar to 10.8-4.92 Ma) sub-group is marked by multistoried sandstones and minor mudstone and mainly weakly developed palaeosols, indicating deposition by large braided rivers in the form of megafans in a Lowland set-up of Thomas et al. (2002). Significant change in nature and size of rivers from the Lower to Middle Siwalik at similar to 10 Ma is found almost throughout of the basin from Kohat Plateau (Pakistan) to Nepal because the Himalayan orogeny witnessed its greatest tectonic upheaval at this time leading to attainment of great heights by the Himalaya, intensification of the monsoon, development of large rivers systems and a high rate of sedimentation, hereby a major change from the Upland set-up to the Lowland set-up over major parts of the HFB. An interesting geomorphic environmental set-up prevailed in the Ramnagar sub-basin during deposition of the studied Upper Siwalik (similar to 4.92 to <1.68 Ma) sediments as observed from the degree of pedogenesis and the type of palaeosols. In general, the Upper Siwalik sub-group in the Ramnagar sub-basin is subdivided from bottom to top into the Purmandal sandstone (4.92-4.49 Ma), Nagrota (4.49-1.68 Ma) and Boulder Conglomerate (<1.68 Ma) formations on the basis of sedimentological characters and change in dominant lithology. Presence of mudstone, a few thin gravel beds and dominant sandstone lithology with weakly to moderately developed palaeosols in the Purmandal sandstone Fm. indicates deposition by shallow braided fluvial streams. The deposition of mudstone dominant Nagrota Fm. with moderately to some well developed palaeosols and a zone of gleyed palaeosols with laminated mudstones and thin sandstones took place in an environment marked by numerous small lakes, water-logged regions and small streams in an environment just south of the Piedmont zone, perhaps similar to what is happening presently in the Upland region/the Upper Gangetic plain. This area is locally called the `Trai region' (Pascoe, 1964). Deposition of Boulder Conglomerate Fm. took place by gravelly braided river system close to the Himalayan Ranges. Activity along the Main Boundary Fault led to progradation of these environments distal-ward and led to development of on the whole a coarsening upward sequence. (C) 2014 Elsevier B.V. All rights reserved.

Ghosts of order on the frontier of chaos

What kinds of motion can occur in classical mechanics? We address this question by looking at the structures traced out by trajectories in phase space; the most orderly, completely integrable systems are characterized by phase trajectories confined to low-dimensional, invariant tori. The KAM theory examines what happens to the tori when an integrable system is subjected to a small perturbation and finds that, for small enough perturbations, most of them survive.

The KAM theory is mute about the disrupted tori, but, for two-dimensional systems, Aubry and Mather discovered an astonishing picture: the broken tori are replaced by "cantori," tattered, Cantor-set remnants of the original invariant curves. We seek to extend Aubry and Mather's picture to higher dimensional systems and report two kinds of studies; both concern perturbations of a completely integrable, four-dimensional symplectic map. In the first study we compute some numerical approximations to Birkhoff periodic orbits; sequences of such orbits should approximate any higher dimensional analogs of the cantori. In the second study we prove converse KAM theorems; that is, we use a combination of analytic arguments and rigorous, machine-assisted computations to find perturbations so large that no KAM tori survive. We are able to show that the last few of our Birkhoff orbits exist in a regime where there are no tori.

Exibição de Propaganda Personalizada com o uso de Realidade Aumentada

É apresentado como problema atual na área de Publicidade e Propaganda a exibição de conteúdo personalizado para nichos específicos. A propaganda acaba se concentrando nos produtos de maior sucesso, tendo como foco alguns públicos-alvo previamente determinados. Assim, o estudo pretende avaliar um novo canal para exibição de propaganda em nível individual, através das perspectivas da Cauda Longa e da Realidade Aumentada (R.A.). O ponto principal desse trabalho é, portanto, mostrar a quantidade de nichos existentes e sugerir uma personalização da propaganda a um nível praticamente individual, como uma ligação direta entre produto e consumidor, usando como suporte tecnológico a R.A. A partir da análise de trabalhos de Romero Tori, Paul Milgram, Ronald Azuma, Cláudio Kirner, Robson Siscouto, Lúcia Santaella, entre outros autores, foi feita uma avaliação dos principais pontos de interesse da tecnologia de Realidade Aumentada para profissionais da área do Design. Discorrendo não só sobre suas características como também identificando problemas e questionamentos atuais, tanto para esses profissionais como para o consumidor final. A tese se enquadra na linha de pesquisa de Design e Tecnologia ao passo que os profissionais desta área de conhecimento são responsáveis diretos por pensar as formas de interação de modo que sejam mais orgânicas e intuitivas para os usuários. Existe muito trabalho a ser realizado, no tocante à Ergonomia e Usabilidade, nas soluções que usam a Realidade Aumentada, principalmente na forma como se dá a sobreposição da informação digital ao ambiente real capturado pela câmera e sua manipulação pelo indivíduo.

Estilos fluviais em bacias de drenagem na Vila Abraão e Vila Dois Rios: uma contribuição à gestão sustentável dos recursos hídricos da Ilha Grande RJ.

Inserida no bioma Mata Atlântica, a Ilha Grande está protegida atualmente por unidades de conservação ambiental definidas por leis, uma vez que é parte importante no cenário ambiental brasileiro. Durante séculos, a Ilha Grande sofreu alterações de diferentes níveis. A desativação do presídio abriu portas para o crescimento descontrolado do turismo, que afetou negativamente as bacias hidrográficas estudadas, deixando-as em evidência. Nesse cenário, o estudo de três bacias de drenagem da Ilha Grande, localizadas na Costa Verde do estado do Rio de Janeiro, buscou compreender a morfologia e a dinâmica dos canais fluviais, por meio de análises das características ambientais, da interferência antrópica e da aplicação do uso do primeiro estágio da metodologia de pesquisa Estilos Fluviais, apontando as partes mais sensíveis às ações antrópicas. Cinco estilos fluviais foram identificados. Os dois primeiros são denominados canais florestados e rochosos, estilos menos frágeis por estarem localizados em áreas de difícil acesso; os trechos com canais meândricos são áreas sensíveis, no entanto, permanecem em boas condições devido à pouca interferência humana, esse estilo foi identificado apenas nos trechos finais dos canais principais das duas bacias da Vila Dois Rios. Os últimos estilos estão presentes na Vila Abraão: os canais assoreados cascalhoarenosos e assoreados arenosos, que apresentam trechos mais críticos por sofrerem interferências antrópicas e por apresentarem uma área com mais sensibilidade. As informações obtidas após esse estudo servirão como base para a elaboração de projetos e pesquisas que visem reabilitar os rios avaliados, assim como seu entorno, e também promover o monitoramento da conservação de áreas ainda preservadas.

Individual grain boundary properties and overall performance of metal-organic-deposition coated conductors

We have investigated single grain boundaries (GBs) isolated in coated conductors produced by Metal-Organic Deposition (MOD). When a magnetic field is swept in the film plane, an angle-dependent crossover from boundary to grain limited critical current density Jc is found. In the force-free orientation, even at fields as high as 8 T, the GBs still limit Jc. We deduce that this effect is a direct consequence of GB meandering. We have employed these single GB results to explain the dependence of Jc of polycrystalline tracks on their width: in-plane measurements become flatter as the tracks are narrowed down. This result is consistent with the stronger GB limitation at field configurations close to force-free found from the isolated boundaries. Our study shows that for certain geometries even at high fields the effect of GBs cannot be neglected.